Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^2-x-7=0
-
Equation x^2+x-9=0
-
Equation -2(-2-y)-y-2=0
-
Equation x+5=13
- Express {x} in terms of y where:
- -6*x-13*y=17
- -7*x+5*y=1
- -6*x-19*y=7
- -19*x-4*y=-19
- Derivative of:
-
cos(4*x)
- Integral of d{x}:
-
cos(4*x)
- Limit of the function:
-
cos(4*x)
-
Identical expressions
- cos(four *x)= one
- co sinus of e of (4 multiply by x) equally 1
- co sinus of e of (four multiply by x) equally one
- cos(4x)=1
- cos4x=1
-
Similar expressions
- sin(2*(x+5*pi)/6)*cos(4*x+pi/2)=1
- cos(x)-sin(x)*cos(4x)=sqr(2)
- d(6x-3cos4x)
cos(4*x)=1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(4 x \right)} = 1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$4 x = \pi n + \operatorname{acos}{\left(1 \right)}$$
$$4 x = \pi n - \pi + \operatorname{acos}{\left(1 \right)}$$
Or
$$4 x = \pi n$$
$$4 x = \pi n - \pi$$
, where n - is a integer
Divide both parts of the equation by
$$4$$
we get the answer:
$$x_{1} = \frac{\pi n}{4}$$
$$x_{2} = \frac{\pi n}{4} - \frac{\pi}{4}$$
$$\cos{\left(4 x \right)} = 1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$4 x = \pi n + \operatorname{acos}{\left(1 \right)}$$
$$4 x = \pi n - \pi + \operatorname{acos}{\left(1 \right)}$$
Or
$$4 x = \pi n$$
$$4 x = \pi n - \pi$$
, where n - is a integer
Divide both parts of the equation by
$$4$$
we get the answer:
$$x_{1} = \frac{\pi n}{4}$$
$$x_{2} = \frac{\pi n}{4} - \frac{\pi}{4}$$
Sum and product of roots
[src]
sum
pi -- 2
$$\frac{\pi}{2}$$
=
pi -- 2
$$\frac{\pi}{2}$$
product
pi 0*-- 2
$$0 \frac{\pi}{2}$$
=
0
$$0$$
0
Numerical answer
[src]
x1 = -28.2743337586152
x2 = -31.4159266517141
x3 = 73.8274274646672
x4 = 43.9822971692691
x5 = 65.9734457525462
x6 = -58.1194640062544
x7 = 45.5530935075531
x8 = -50.2654823342013
x9 = -59.6902604569585
x10 = -20.4203521774723
x11 = 34.5575190717885
x12 = -89.5353907315491
x13 = 21.9911485851564
x14 = -81.6814090370675
x15 = 1.57079638652515
x16 = -94.247779486083
x17 = -344.004395625893
x18 = 20.4203521581227
x19 = 86.3937978937855
x20 = 42.4115007365289
x21 = 89.5353906153414
x22 = -61.2610566398387
x23 = 87.9645943351391
x24 = -87.9645943594276
x25 = -1.57079626356835
x26 = 72.2566310277248
x27 = -21.9911485864927
x28 = -97.3893725907902
x29 = 7.85398173011892
x30 = 81.6814091152362
x31 = -72.2566309100272
x32 = 95.8185760424586
x33 = 59.690260541069
x34 = -64.402649310466
x35 = -14.1371668484631
x36 = 95.8185756842062
x37 = -6.28318518328035
x38 = -23.5619449982306
x39 = 117.809724442492
x40 = -29.8451301000724
x41 = 0.0
x42 = -9.42477807759933
x43 = -53.4070752253874
x44 = -86.3937978789102
x45 = -42.4115007432387
x46 = 36.1283154718409
x47 = 26.7035375390573
x48 = -75.3982237985682
x49 = -95.818575868455
x50 = 14.1371670778185
x51 = 72.256630710694
x52 = -36.128315427252
x53 = -43.9822971747455
x54 = 12.5663704969137
x55 = 51.8362788866811
x56 = 92.6769832182628
x57 = -100.530965206253
x58 = 48.6946860958663
x59 = -45.5530935761698
x60 = 67.5442420634706
x61 = 78.5398162225044
x62 = -97.3893723711949
x63 = -15.7079632962205
x64 = 4.71238898608896
x65 = 64.4026493150839
x66 = 70.6858346557926
x67 = 50.2654824463816
x68 = 100.530964798296
x69 = 23.5619449483644
x70 = 37.6991119665793
x71 = -67.5442421539445
x72 = 28.2743338652921
x73 = -83.2522051669813
x74 = -80.1106125854791
x75 = 6.28318528443138
x76 = -37.6991118766796
x77 = -17.2787595621355
x78 = 29.8451303084991
x79 = 56.5486676469942
x80 = -51.8362786915081
x81 = -1.57079642013166
x82 = 15.7079633917898
x83 = -73.8274272808521
x84 = -7.85398150696156
x85 = -65.9734457653935
x86 = -39.2699081045218
x87 = 94.247779609353
x87 = 94.247779609353
The graph